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The members of every collection possess some quality common to them and possessed by nothing else in the universe; and for that reason it is for some purposes much the same thing to say that an object belongs to a collection and to say that it possesses a quality. But for other purposes the distinction is important. Qualities possess no individual identity but only similarity while a collection is a single individual collection, though possessing it is true only a derived individuality.
A quality possesses, in itself, few positive qualities, which few are mostly of the particular kind called quantities. Thus, any particular kind of red, has its degree of light, its degree of fullness of color, and its peculiar quality of hue. This third is something more than a mere quantity.
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But it varies only in two opposite ways like a quantity. A collection, on the other hand, bas all sorts of qualities discoverable by experience. Thus, a man's body is a collection of molecules; and its qualities are what is true of some of these molecules in relation to each other and to other things. Multitude is a quality of a collection or something like that; and accordingly it possesses only one quality which is its quantity. It consists in the collection's being more than some and less than others. But I do not know
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Ladies and Gentlemen:
The alpha part of graphs, of which I gave you a tolerably full account, although without illustrating the use of it, since there was no time for that, is able to deal with represent no reasonings except those which turn upon the logical relations of general terms.
The beta part of which I was able to give you nothing more than a few scraps has been thoroughly elaborated. It is able to handle with facility and dispatch reasonings of a very intricate kind, and propositions